Question

Calculating Profitability Index What is the profitability index for the following set of cash flows if the relevant discount rate is 10 percent? What if the discount rate is 15 percent? If it is 22 percent?  

Year	Cash Flow
0	-$29,500
1	16,900
2	13,600
3	8,300

Answer 1

To calculate the PI, we need to calculate the NPV:

When discount rate = 10%

Year	CF	Discount Factor	Discounted CF
0	$     -29,500.00	1/(1+0.1)^0=	1	1*-29500=	$   -29,500.00
1	$       16,900.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*16900=	$     15,363.64
2	$       13,600.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*13600=	$     11,239.67
3	$         8,300.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*8300=	$       6,235.91
				NPV = Sum of all Discounted CF	$       3,339.22
				Profitability Index	1.11

When discount rate = 15%

Year	CF	Discount Factor	Discounted CF
0	$     -29,500.00	1/(1+0.15)^0=	1	1*-29500=	$   -29,500.00
1	$       16,900.00	1/(1+0.15)^1=	0.869565217	0.869565217391304*16900=	$     14,695.65
2	$       13,600.00	1/(1+0.15)^2=	0.756143667	0.756143667296787*13600=	$     10,283.55
3	$         8,300.00	1/(1+0.15)^3=	0.657516232	0.657516232431988*8300=	$       5,457.38
				NPV = Sum of all Discounted CF	$           936.59
				Profitability Index	1.03

When discount rate = 22%

Year	CF	Discount Factor	Discounted CF
0	$     -29,500.00	1/(1+0.22)^0=	1	1*-29500=	$   -29,500.00
1	$       16,900.00	1/(1+0.22)^1=	0.819672131	0.819672131147541*16900=	$     13,852.46
2	$       13,600.00	1/(1+0.22)^2=	0.671862403	0.671862402579952*13600=	$       9,137.33
3	$         8,300.00	1/(1+0.22)^3=	0.550706887	0.550706887360616*8300=	$       4,570.87
				NPV = Sum of all Discounted CF	$     -1,939.35
				Profitability Index	0.93